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Stability Analysis of Equilibrium Manifolds for a Two-Predators One-Prey Model 被引量：1

Stability Analysis of Equilibrium Manifolds for a Two-Predators One-Prey Model
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摘要 The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed. The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed.
作者 张鑫 唐云 Rudolf Scherer
机构地区 Department of Mathematical Sciences Institute of Practical Mathematics
出处 《Tsinghua Science and Technology》 SCIE EI CAS 2006年第6期739-744,共6页 清华大学学报（自然科学版（英文版）
基金 Supported by the National Natural Science Foundation of China (No. 10272059)
关键词 BIFURCATION equilibrium manifold predator-prey model STABILITY bifurcation equilibrium manifold predator-prey model stability
分类号 O175.13 [理学—基础数学]
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参考文献9

  • 1Sze-Bi Hsu,Tzy-Wei Hwang,Yang Kuang.Rich dynamics of a ratio-dependent one-prey two-predators model[J].Journal of Mathematical Biology.2001(5)
  • 2Sze-Bi Hsu,Tzy-Wei Hwang,Yang Kuang.Global analysis of the Michaelis–Menten-type ratio-dependent predator-prey system[J].Journal of Mathematical Biology.2001(6)
  • 3Robinson C.Dynamical Systems, Stability, Symbolic Dy- namics and Chaos ([]..1998
  • 4Lee J,,Chiang H-D.Theory of stability regions for a class of nonhyperbolic dynamical systems and its application to constraint satisfaction problems[].IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applica- tions.2002
  • 5Fiedler B,,Liebscher S.Generic Hopf bifurcation from lines of equilibria without parameters: Ⅱ, Systems of vis- cous hyperbolic balance laws[].SIAM Journal on Mathematical Analysis.2000
  • 6Hsu Sze-Bi,,Hwang Tzy-Wei,Kuang Yang.A ratio- dependent food chain model and its applications to bio- logical control[].Mathematical Biosciences.2003
  • 7Fiedler B,Liebscher S.Bifurcations without parameters: Some ODE and PDE examples[].ICM.2002
  • 8Fiedler B,,Liebscher S,Alexander J C.Generic Hopf bi- furcation from lines of equilibria without parameters: I, Theory[].Journal of Differential Equations.2000
  • 9Fiedler B,,Liebscher S,Alexander J C.Generic Hopf bi- furcation from lines of equilibria without parameters: Ⅲ, Binary oscillations[].International Journal of Bifurcation and Chaos.2000

同被引文献6

  • 1Aulbach B. Continuous and discrete dynamics near manifolds of equilibra[M]//Lecture notes in math: 1058. New York: Springer-Verlag, 1984.
  • 2Fiedler B, Liebscher S, Alexander J C. Generic Hopf bifurcation from lines of equilibria without parameters I:Theory [J]. J Diff Equs,2000,167:16.
  • 3Fiedler B, Liebscher S. Generic Hopf bifurcation from lines of equilibria without parameters II: Systems of viscous hyperbolic balance laws[J]. SIAM J Math Anal,2000,31(6) :1396.
  • 4Fiedler B,Liebscher S, Alexander J C. Generic Hopf bifurcation from lines of equilibria without parameters Ⅲ:Binary osciUations[J]. Int J Bifur & Chaos,2000,10(7) : 1613.
  • 5Fiedler B,Liebscher S. Bifurcations without parameters: some ODE and PDE examples[C]//Proceedings of the International Congress of MathematiciansⅢ. Beijing: Higher Ed Press, 2002,3,305.
  • 6Hsu Sze-bi, Hwang Tzy-wei, Kuang Yang. Rich dynamics of a ratio-dependent one-prey two-predators model[J]. J Math Biol,2001,43:377.

引证文献1

Tsinghua Science and Technology
2006年 第6期

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